Depends on where you live. If you are downtown (Vesturbær, Miðbær, Austurbær), most places are accessible by foot or biking. Anywhere else wll probably be hard or impossible to get around on foot to places of interest.
The bus system here is abysmal compared to other Nordic countries, but can still be used and is okay once you get accustomed to it. If you are further away from the center, like Grafarvogur or Hafnarfjörður, driving is a lot more convenient than taking a bus since the schedules aren't very forgiving.